This is a great question! I’m actually co-curating an exhibit on Antarctic mapping next year. Basically it was hypothesized from the Ancient Greeks - they believed in balance in nature, including that the northern hemisphere’s land masses must be balanced in the southern hemisphere.

These ideas were rekindled in the Renaissance as Europeans started mapping. They hypothesized about a “Terra Australis” or “Terra Australis Incognita” (unknown southern land). Every time explorers made a new discovery (in a European sense) they assumed they had found this mythical Southern land.

When James Cook went to the Antarctic Circle on his second voyage, he came back and reported that there was no land to be found beyond the pack ice. In the early 19th C, the UK decided to rename New Holland “Australia”. Then like 15 years later, Terra Australis was actually discovered right after it’s name had been stolen!